// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2013-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_REALSVD2X2_H
#define EIGEN_REALSVD2X2_H

namespace Eigen {

namespace internal {

template<typename MatrixType, typename RealScalar, typename Index>
void
real_2x2_jacobi_svd(const MatrixType& matrix,
					Index p,
					Index q,
					JacobiRotation<RealScalar>* j_left,
					JacobiRotation<RealScalar>* j_right)
{
	using std::abs;
	using std::sqrt;
	Matrix<RealScalar, 2, 2> m;
	m << numext::real(matrix.coeff(p, p)), numext::real(matrix.coeff(p, q)), numext::real(matrix.coeff(q, p)),
		numext::real(matrix.coeff(q, q));
	JacobiRotation<RealScalar> rot1;
	RealScalar t = m.coeff(0, 0) + m.coeff(1, 1);
	RealScalar d = m.coeff(1, 0) - m.coeff(0, 1);

	if (abs(d) < (std::numeric_limits<RealScalar>::min)()) {
		rot1.s() = RealScalar(0);
		rot1.c() = RealScalar(1);
	} else {
		// If d!=0, then t/d cannot overflow because the magnitude of the
		// entries forming d are not too small compared to the ones forming t.
		RealScalar u = t / d;
		RealScalar tmp = sqrt(RealScalar(1) + numext::abs2(u));
		rot1.s() = RealScalar(1) / tmp;
		rot1.c() = u / tmp;
	}
	m.applyOnTheLeft(0, 1, rot1);
	j_right->makeJacobi(m, 0, 1);
	*j_left = rot1 * j_right->transpose();
}

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_REALSVD2X2_H
